Let us first consider subset sum and knapsack for free abelian groups \(\mathbb {Z}^m\) . Note that
\(\mathbb {Z}^m\)  is isomorphic to the graph group \(\mathbb {G}(A,I)\)  where \((A,I)\)  is the
complete graph on \(m\)  nodes. Our first result is a simple combination of known
results [1]}, [2]}.
